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Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 21.3 Circles to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 21.3 Circles

Exercises

SOLVE

Question 1.
What is the diameter of the circle?

Answer:
The diameter of the circle is equal to 2 cms,

Explanation:
As we know the diameter of the circle is equal to 2 X radius, so as the given circle has
r = 1 cm so diameter = 2 x 1 cm = 2 cms.

Question 2.
What is the diameter of the circle?

Answer:
The diameter of the circle is equal to 14 in.,

Explanation:
As we know the diameter of the circle is equal to 2 X radius, so as the given circle has
r = 1 cm so diameter = 2 x 7 in. = 14 inches.

Question 3.
What is the radius of the circle below?

Answer:
The radius of the circle is equal to 4 ft,

Explanation:
As we know the diameter of the circle is equal to 2 X radius, so as the given circle has
d = 8 ft so radius = diameter/ 2 = 8 ft/2 = 4 ft.

Question 4.
What is the center of the circle?

Answer:
The center of the circle is d/2,

Explanation:
As we know the diameter of the circle is equal to 2 X radius so as the given circle has
diameter = 2 x radius or center, therefore center = d/2.

Question 5.
What is the radius of the circle?

Answer:
The radius of the circle is equal to 3 in.,

Explanation:
As we know the diameter of the circle is equal to 2 X radius, so as the given circle has
d = 6 in. so radius = diameter/ 2 = 6 in/2 = 3 in.

Question 6.
What are the two radii of the circle?

Answer:
OA,OB,

Explanation:
As a Radius or Radii of a circle is the distance from the center of the circle to any point on it’s circumference. So the given circle has two radii they are OA and OB.

SOLVE

Question 1.

What is the area of the circle? ___________
What is the circumference? ___________
Answer:
The area of the circle is 314.285 cm²,
The circumference of the circle is 62.857 cm,

Explanation:
Given the diameter of the circle as 20 cm as we know the diameter of the circle is equal to 2 X radius, so as the given circle has d = 20 cm so radius = diameter/ 2 = 20 cm/2 = 10 cm. We know area of the circle as A = π r², A = 3.14285 X 10 cm X 10 cm = 314.285 cm² and circumference of the circle is C = 2πr = 2 X 3.14285 X 10 cm = 62.857 cm.

Question 2.

What is the circumference of the circle? ___________
What is the radius? ___________
Answer:
The circumference of the circle is 14 π,
The radius is 7,

Explanation:
Given the area of the circle as 49π as we know area of the circle as A = π r²,
49 π = π X r X r, So r= square root of 49 so r = 7 and as circumference of the circle is C = 2πr = 2 X π X 7 = 14π.

Question 3.

What is the diameter of the circle? ___________
What is the area? ___________
What is the circumference? ___________
Answer:
The diameter of the circle is equal to 10 cm,
The area of the circle is 78.57125 cm²,
The circumference of the circle is 31.4285 cm,

Explanation:
As we know the diameter of the circle is equal to 2 X radius given r = 5 cm so as the given circle has d = 2 X 5 cm = 10 cm. As we know area of the circle as A = π r², A = 3.14285 X 5 cm X 5 cm = 78.57125 cm² and circumference of the circle is C = 2πr = 2 X 3.14285 X 5 cm = 31.4285 cm.

Question 4.

What is the circumference of the circle? ___________
What is the area of the circle? ___________
Answer:
The circumference of the circle is 37.7142 cm,
The area of the circle is  113.1426 cm²,

Explanation:
As we know the diameter of the circle is equal to 2 X radius given d = 12 cm so as the given circle has r = 12/2 cm = 6 cm. As we know circumference of the circle is C = 2πr = 2 X 3.14285 X 6 cm = 37.7142 cm and area of the circle as A = π r², A = 3.14285 X 6 cm X 6 cm = 113.1426 cm².

Question 5.
A bicycle wheel measures 25 inches in diameter. How far would a bike travel if the wheel went completely around 4 times?
____________ inches
Answer:
Far would a bike travel if the wheel went completely around 4 times is 78.57125 inches,

Explanation:
Given A bicycle wheel measures 25 inches in diameter. Far would a bike travel if the wheel went completely around 4 times as we know the diameter of the circle is equal to 2 X radius given d = 25 inches so as the given circle has r = 25/2 inches = 12.5 inches. As we know circumference of the circle is C = 2πr = 2 X 3.14285 X 12.5 inches = 78.57125 inches.

Question 6.
Brenda walks her dog along two circular routes laid out in the park. How much longer is Route B then route A? (Leave the answer in terms of pi.)

_____________ π km
Answer:
Longer is route B than route A is 10π km,

Explanation:
Given Brenda walks her dog along two circular routes laid out in the park. Much longer is Route B then route A is as circumference of route A is 2πr as r is 5 km so it is 2 X π X 5 km = 10π km and circumference of route B is 2πr as r is 10 km so it is 2 X π X 10 km = 20π km therefore longer is route B than route A is 20π km – 10π km = 10π km.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 21.2 Polygons to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 21.2 Polygons

Exercises

IDENTIFY

Indicate whether the figure is a polygon. Write “Polygon” or “Not a Polygon”.

Question 1.

Answer:
Polygon,

Explanation:
The given shape is a polygon as it is a closed 2-dimensional figure made up of line segments and it has more than 3 sides.

Question 2.

Answer:
Polygon,

Explanation:
The given shape is a polygon as it is a closed 2-dimensional figure made up of line segments and it has more than 3 sides.

Question 3.

Answer:
Polygon,

Explanation:
The given shape is a polygon as it is a closed 2-dimensional figure made up of line segments and it has more than 3 sides.

Question 4.

Answer:
Polygon,

Explanation:
The given shape is a polygon as it is a closed 2-dimensional figure made up of line segments and it has more than 3 sides.

Question 5.

Answer:
Not a Polygon,

Explanation:
The given shape is a not polygon as it is a closed 2-dimensional figure made up of not only line segments but also with curves.

Question 6.

Answer:
Polygon,

Explanation:
The given shape is a polygon as it is a closed 2-dimensional figure made up of line segments and it has more than 3 sides.

Question 7.

Answer:
Polygon,

Explanation:
The given shape is a polygon as it is a closed 2-dimensional figure made up of line segments and it has more than 3 sides.

Question 8.

Answer:
Polygon,

Explanation:
The given shape is a polygon as it is a closed 2-dimensional figure made up of line segments and it has more than 3 sides.

Question 9.

Answer:
Polygon,

Explanation:
The given shape is a polygon as it is a closed 2-dimensional figure made up of line segments and it has more than 3 sides.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 21.1 Quadrilaterals to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 21.1 Quadrilaterals

Exercises

IDENTIFY

For each figure below, label as a square, rectangle, rhombus, trapezoid, or kite.

Question 1.

Answer:
Square,

Explanation:
We know if all the four sides are of the same length it is a square, as we have given shape have with all the four sides 4 in. so it is a square.

Question 2.

Answer:
Trapezoid,

Explanation:
As a trapezoid has two opposite sides that are parallel, but the sides are not the same
length and the other two sides of a trapezoid are not parallel, So given shape is trapezoid.

Question 3.

Answer:
Rectangle,

Explanation:
As the given shape has 2-dimensional figure with four right angles and the opposite sides are parallel and the same length so it is rectangle.

Question 4.

Answer:
Rectangle,

Explanation:
As the given shape has 2-dimensional figure with four right angles and the opposite sides are parallel with the same length a,a and b,bso it is rectangle.

Question 5.

Answer:
Trapezoid,

Explanation:
As a trapezoid has two opposite sides that are parallel, but the sides are not the same
length and the other two sides of a trapezoid are not parallel, So given shape is trapezoid.

Question 6.

Answer:
Square,

Explanation:
We know if all the four sides are of the same length it is a square, as we have given shape have with all the four sides equal so it is a square.

Question 7.

Answer:
Rhombus,

Explanation:
Given shape is rhombus with opposite sides are parallel and all the sides are the same length. Unlike a rectangle, a rhombus does not have four right angles.

Question 8.

Answer:
Kite,

Explanation:
Given shape is a kite as it is a quadrilateral which looks like a typical toy kite, so it is a kite, two of its angles are equal, Its longer two touching sides are equal in length and so
are shorter two touching sides.

Question 9.

Answer:
Rectangle,

Explanation:
As the given shape has 2-dimensional figure with four right angles and the opposite sides are parallel and the same length so it is rectangle.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 20.3 Right Triangles and Pythagorean Theorem to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 20.3 Right Triangles and Pythagorean Theorem

Exercises

SOLVE

Use the Pythagorean Theorem to determine the length of the missing side.

Question 1.
If side A is 6 and side B is 8, then side C (the hypotenuse) is _____________
Answer:
C = 10,

Explanation:
As side A is 6 and side B is 8, then side C (the hypotenuse) is applying Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So C = square root of (A² + B² ) = square root of (6² + 8²)= square root of (36 + 64) = square root of 100 = 10.

Question 2.
If side A is 9 and side B is 9, then side C (the hypotenuse) is _____________
Answer:
C = 12.72,

Explanation:
As side A is 9 and side B is 9, then side C (the hypotenuse) is applying Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So C = square root of (A² + B² ) = square root of (9² + 9²)= square root of (81 + 81) = square root of 162 , approximately equal to 12.72.

Question 3.
If side A is 10 and side B is 24, then side C (the hypotenuse) is _____________
Answer:
C = 26,

Explanation:
As side A is 10 and side B is 24, then side C (the hypotenuse) is applying Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So C = square root of (A² + B² ) = square root of (10² + 24²)= square root of (100 + 576) = square root of 676 = 26.

Question 4.
If side A is 9 and side C (the hypotenuse) is 15, then side B is _____________
Answer:
B = 12,

Explanation:
As side A is 9 and side C (the hypotenuse) is 15, then side B is applying Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. C = square root of (A² + B² ) therefore B = square root of (C^{2 –} A²)= square root of (225 – 81) = square root of 144 = 12.

Question 5.
If side B is 6 and the hypotenuse is 10, then side A is _____________
Answer:
A = 8,

Explanation:
As side B is 6 and the hypotenuse is 10, then side A is applying Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So C = square root of (A² + B² ) therefore A = square root of (C² – B²)= square root of (100 – 36) = square root of 64 = 8.

Question 6.
If side A is 12 and side B is 5, then side C (the hypotenuse) is _____________
Answer:
C = 13,

Explanation:
As side A is 12 and side B is 5, then side C (the hypotenuse) is applying Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So C = square root of (A² + B² ) = square root of (12² + 5²) = square root of (144 + 25) = square root of 169 = 13.

Find the missing sides of the following pairs of similar right triangles:

Question 1.
HI = ___________ ft
KL = ___________ ft
JL = ____________ ft

Answer:
HI = 50 ft.,
KL = 30 ft.,
JL =  78 ft.,

Explanation:
For finding HI we apply Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So HI = square root of (GI² – GH² ) = square root of (130² – 120²) = square root of (16,900 – 14,400) = square root of 2,500 = 50 ft.
Now finding KL let it be x as GHI and JKL are similar triangles that means the ratios of the sides are equal  HI/GH = KL/JK = 50/120 = x/72 cross multiplying for the unknown we get
120x = 50 X 72, x = 5 X 72/12 = 5 X 6 = 30 ft.
Now JL we apply Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So HI = square root of (JK² + KL² ) = square root of (72² + 30²) = square root of (5,184 + 900) = square root of 6,084 = 78 ft.

Question 2.
LN = ___________ m
PQ = ___________ m
OQ = ____________ m

Answer:
LN = 25 ft., = 7.62 m,
PQ = 21 ft., = 6.4008 m,
OQ = 35 ft., = 10.668 m,

Explanation:
For finding LN we apply Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So LN = square root of (LM² + MN² ) = square root of (20² + 15²) = square root of (400 + 225) = square root of 625 = 25 ft. As 1 foot is equal to 0.3048 meter,
so 25 X 0.3048 m = 7.62 m.
Now finding PQ let it be x as LMN and OPQ are similar triangles that means the ratios of the sides are equal  MN/LM = PQ/OP = 15/20 = x/28 cross multiplying for the unknown we get
20x = 15 X 28, x = 3 X 28/4 = 3 X 7 = 21 ft., = 21 X 0.3048 m = 6.4008 m.
Now OQ we apply Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So OQ = square root of (OP² + PQ² ) = square root of (28² + 21²) = square root of (784 + 441) = square root of 1,225 = 35 ft., = 35 X 0.3048 m =  10.668 m.

Question 3.
RT = ___________ in.
VW = ___________ in.
UW = ____________ in.

Answer:
RT = 7.071 ft., = 84.852 in.,
VW = 20 ft., = 240 in.,
UW = 28.284 ft., = 339.400 in.,

Explanation:
For finding RT we apply Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So HI = square root of (RS² + ST² ) = square root of (5² + 5²) = square root of (25 + 25) = square root of 50 = 7.071 ft. As 1 foot is equal to 12 inch we get 7.071 X 12 inch = 84.852 in, Now finding VW let it be x as RST and UVW are similar triangles that means the ratios of the sides are equal  ST/RS = VW/UV = 5/5 = x/20 cross multiplying for the unknown we get 5x = 5 X 20, x = 20 ft., = 20 X 12 in = 240 in.,
Now UW we apply Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So UW = square root of (UV² + VW² ) = square root of (20² + 20²) = square root of (400 + 400) = square root of 800 = 28.284 ft., = 339.408 in.

Question 4.
If the two triangles are similar, then what is the length of the missing side?

Answer:
The length of the missing side is 16 ft.,

Explanation:
As given two triangles are similar triangles that means the ratios of the sides are equal, Let the missing side be x so 9/12 = 12/x cross multiplying for the unknown we get 9x = 12 X 12, x = 12 X 12/9 = 12 X 4 /3 = 4 X 4 = 16 ft.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 18.2 Line Segments and Rays to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 18.2 Line Segments and Rays

Exercises

SOLVE

Question 1.
Draw a diagram that illustrates a ray \(\overrightarrow{Y X}\).
Answer:

Explanation:
Drawn a diagram that illustrated a ray \(\overrightarrow{Y X}\) as shown above.

Question 2.
Identify two rays and two line segments in the figure.

Answer:
Two rays: \(\overrightarrow{XL}\), \(\overrightarrow{YM}[/latex,Two line segments: LX,YM

Explanation:
Identified two rays [latex]\overrightarrow{XL}\), \(\overrightarrow{YM}\) as rays means a part of a line that has one endpoint and goes on infinitely in only one direction. Two line segments LX, YM as in geometry, a line segment is bounded by two distinct points on a line also a line segment is part of the line that connects two points.

Question 3.
Identify three line segments in the diagram.

Answer:
Three line segments: AB, BC, CD,

Explanation:
The three line segments in the given diagram above are AB, BC, CD.

Question 4.
Draw two rays \(\overrightarrow{A B}\) and \(\overrightarrow{A C}\).
Answer:

Explanation:
Drawn two rays \(\overrightarrow{A B}\) and \(\overrightarrow{A C}\) as shown above.

Question 5.
Identify the two line segments.

Answer:
CD, PN,

Explanation:
Identified the given line segments CD, PN as a line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects two points.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 20.2 Triangles: Congruent and Similar to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 20.2 Triangles: Congruent and Similar

Exercises

IDENTIFY

Identify each set of triangles as similar, congruent, or neither. Explain your answer.

Question 1.

Answer:
Congruent Triangles,

Explanation:
Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.  Given triangles have equal sides and equal angles
therefore they are congruent.

Question 2.

Answer:
Neither,

Explanation:
Given triangles have one common angle and lengths but they have different angles so they are neither congruent nor all similar angles.

Question 3.

Answer:
Congruent Triangles,

Explanation:
Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.  Given triangles have equal sides and equal angles
therefore they are congruent.

Question 4.

Answer:
Similar Triangles,

Explanation:
Similar triangles are triangles with same shape but with different sizes and also with same
angles. So given triangles are similar.

Question 5.

Answer:
Similar Triangles,

Explanation:
Similar triangles are triangles with same shape but with different sizes and also with same
angles. So given triangles are similar.

Question 6.

Answer:
Congruent Triangles,

Explanation:
Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.  Given triangles have equal sides and equal angles
therefore they are congruent.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 20.1 Triangles: Acute, Right, Obtuse, Equilateral, Isosceles, and Scalene to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 20.1 Triangles: Acute, Right, Obtuse, Equilateral, Isosceles, and Scalene

Exercises

IDENTIFY

Identity as acute, right, or obtuse.

Question 1.

Answer:
Acute Triangle,

Explanation:
An acute angle triangle (or acute-angled triangle) is a triangle in which all the interior angles are acute angles or an acute angle is an angle that is less than 90°.
Given triangle has all interior angles, so it is acute triangle.

Question 2.

Answer:
Obtuse Triangle,

Explanation:
An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. Given triangle one of interior angle measures
more than 90° degrees, so it is obtuse triangle.

Question 3.

Answer:
Right Triangle,

Explanation:
A right angled triangle is a triangle with one of the angles as 90 degrees.
As given triangle has one angle 90 degress so it is right triangle.

Question 4.

Answer:
Acute Triangle,

Explanation:
An acute angle triangle (or acute-angled triangle) is a triangle in which all the interior angles are acute angles or an acute angle is an angle that is less than 90°.
Given triangle has interior angles less than 90 degress so it is acute triangle.

Question 5.

Answer:
Right Triangle,

Explanation:
A right angled triangle is a triangle with one of the angles as 90 degrees.
As given triangle has one angle 90 degress, so it is right triangle.

Question 6.

Answer:
Acute Triangle,

Explanation:
An acute angle triangle (or acute-angled triangle) is a triangle in which all the interior angles are acute angles or an acute angle is an angle that is less than 90°.
Given triangle has all interior angles are acute.

Identify as isosceles, scalene, or equilateral.

Question 7.

Answer:
Equilateral Triangle,

Explanation:
All the given sides are 4 and equal so given triangle is equilateral triangle.

Question 8.

Answer:
Isosceles Triangle,

Explanation:
As given triangle has 2 sides with 8 and one side with 4 lengths so it is an isosceles triangle. As an isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.

Question 9.

Answer:
Scalene Triangle,

Explanation:
Given triangle is a scalene triangle as it has different side lengths so it is
scalene triangle, A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures. However, the sum of all the interior angles is always equal to 180 degrees.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 2.2 Problem Solving to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 2.2 Problem Solving

Exercises Solve

Question 1.
Don volunteers 18 hours a week at the local hospital. If he volunteered 45 weeks last year, how many hours did he spend volunteering?
Answer:
810 hours,

Explanation:
As Don volunteers 18 hours a week at the local hospital. If he volunteered 45 weeks last year, Number of many hours did he spend volunteering are 18 hours X 45 = 810 hours.

Question 2.
Milos can ride his bicycle an average of 81 miles a day. If he wants to visit his cousin 324 miles away, how many days will it take for him to ride there?
Answer:
4 days,

Explanation:
As Milos can ride his bicycle an average of 81 miles a day. If he wants to visit his cousin 324 miles away, Number of days will it take for him to ride there are 324 divided by 81 is
81)324(4
    324
0     , Therefore 4 days.

Question 3.
Lorraine’s cell phone plan allows for 1,200 minutes of free usage every month. During the month of March (March has 31 days), how many minutes a day can Lorraine talk without exceeding her monthly limit?
Answer:
38 minutes 22 seconds,

Explanation:
Given Lorraine’s cell phone plan allows for 1,200 minutes of free usage every month. During the month of March (March has 31 days), Number of minutes a day can Lorraine talk without exceeding her monthly limit 1,200 minutes divided by 31 is
31)1,200(38
     114
     060
      38
22
therefore 38 minutes 22 seconds.

Question 4.
Basil launched his website this year. During the first three months of operation, his site recorded 835,884 hits. If he maintains that same monthly average, how many hits should he expect by the end of the fifteenth month?
Answer:
4,179,420 hits,

Explanation:
As Basil launched his website this year. During the first three months of operation, his site recorded 835,884 hits. If he maintains that same monthly average, Number of hits should he expect by the end of the fifteenth month is 15 divided by 3 is 5 So hits are
1,2,4,4,2
835,884
       X 5
4,179,420.

Question 5.
Camille is counting the number of bricks she needs to build a retaining wall for her herb garden. She calculates that she will need 485 bricks to complete the project. If the bricks come in stacks of 24, how many stacks will she need to complete the project?
Answer:
20 stacks and 5 bricks,

Explanation:
As Camille is counting the number of bricks she needs to build a retaining wall for her herb garden. She calculates that she will need 485 bricks to complete the project. If the bricks come in stacks of 24, Number of many stacks will she need to complete the project is
24)485(20
      480
          5
So 20 stacks and 5 bricks.

Question 6.
Iris volunteered to register voters for an upcoming election. She was able to sign up 374 new voters in just 1 voting precinct. If there are 11 precincts in the town, and Iris expects to have the same amount of success in each precinct, how many new voters will she sign up before the election?
Answer:
38 voters,

Explanation:
Given Iris volunteered to register voters for an upcoming election.
She was able to sign up 374 new voters in just 1 voting precinct.
If there are 11 precincts in the town, and Iris expects to have the same amount of
success in each precinct, Number of many new voters will she sign up before the election
11)374(38
     374
0
38 voters.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 2.1 Multiplying and Dividing Whole Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 2.1 Multiplying and Dividing Whole Numbers

Exercises Multiply

Question 1.

Answer:
2,820,

Explanation:
1
235
X 12
0470
2350
2,820

Question 2.

Answer:
3,652,

Explanation:
332
X 11
0332
3320
3,652

Question 3.

Answer:
3,363,

Explanation:
6,6
177
X 19
1,593
1,770
3,363

Question 4.

Answer:
5,720,

Explanation:
1
44
X 130
0000
1320
4400
5,720

Question 5.

Answer:
84,210,

Explanation:
401
X 210
00000
04010
80200
84,210

Question 6.

Answer:
31,049

Explanation:
5
509
X 61
00509
30540
31,049

Question 7.

Answer:
11,343,

Explanation:
597
X 19
05373
05970
11,343

Question 8.

Answer:
17,922,

Explanation:
618
X 29
05,562
12,360
17,922

Question 9.
Ariel earns money by mowing lawns in his neighborhood. If he can mow 3 lawns in an hour, how many lawns can he mow working 30 hours a week?
Answer:
90 lawns in a week,

Explanation:
Given Ariel earns money by mowing lawns in his neighborhood.
If he can mow 3 lawns in an hour, Number how many lawns can he mow working 30 hours a week is 30 X 3 lawns = 90 lawns in a week.

Question 10.
Winona is tracking the amount of water that the people of her town use during the summer months. She calculates that 47,005 gallons of water are used every day. If Wmona tracks the water usage for 112 days, how much water will be used during that time?
Answer:
52,64,560 gallons of water,

Explanation:
As Winona is tracking the amount of water that the people of her town use during the summer months. She calculates that 47,005 gallons of water are used every day. If Wmona tracks the water usage for 112 days, how much water will be used during that time is 47,005 X 112 = 52,64,560 gallons of water.

Exercises Divide

Question 1.

Answer:
156 R7,

Explanation:
Given to divide 1255 by 8 we get
8)1255(156
   08
    45
    40
      55
      48
        7
so it is 156R7.

Question 2.

Answer:
1,274R1,

Explanation:
Given to divide 15,289 by 12 we get
12) 15,289(1,274
      12
        32
        24
        088
          84
             49
             48
                1
So it is 1,274R1.

Question 3.

Answer:
83R43,

Explanation:
Given to divide 4,027 by 48 we get
48) 4027(83
      384
       187
        144
          43
So it is 83R43.

Question 4.

Answer:
144R5,

Explanation:
Given to divide 1,301 by 9 we get
9)1,301(144
      09
       40
       36
          41
          36  
So it is 144R5.

Question 5.

Answer:
47R10,

Explanation:
Given to divide 715 by 15 we get
15)715(47
      60
       115
        105
          10
So it is 47R10.

Question 6.

Answer:
33R7,

Explanation:
Given to divide 403 by 12 we get
12) 403(33
      36
       43
       36
         7
So it is 33R7.

Question 7.

Answer:
107,

Explanation:
Given to divide 321 by 3 we get
3)321(107
    30
     21
     21
      0
So it is 107.

Question 8.

Answer:
85,

Explanation:
Given to divide 425 by 5 we get
5)425(85
    40
     25
     25
      0
So it is 85.

Question 9.
Aubrey wants to divide his penny collection equally among his 14 cousins. ¡f he has 1,722 pennies in his collection, how many pennies will each one of his cousinš receive?
Answer:
Each one of his cousinš receive 123 pennies,

Explanation:
As Aubrey wants to divide his penny collection equally among his 14 cousins.
If he has 1,722 pennies in his collection, Number of pennies will each one of
his cousinš receive are 14 divides 1,722 are
14)1,722(123
      14
         32
         28
         42
42
0
123 pennies.

Question 10.
Emily wants to bring candy to share with her class at school. If she has 210 pieces of candy, and there are 30 students in her class, how many pieces of candy will each student receive?
Answer:
7 pieces of candy will each student receive,

Explanation:
As Emily wants to bring candy to share with her class at school. If she has 210 pieces of candy, and there are 30 students in her class, Number of pieces of candy will each student receive are 210 divides by 30 we get
30)210(7
     210
0
7 pieces of candy.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 19.3 Finding Missing Angle Measurements to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 19.3 Finding Missing Angle Measurements

Exercises

SOLVE

Question 1.
Fill in the angle measurements for the other seven angles.

∠a = _________
∠b = _________
∠c = _________
∠d = _________
∠e = _________
∠f = _________
∠g = _________
Answer:
∠a = 108⁰, 
∠b = 72⁰,
∠c = 108⁰,
∠d = 72⁰,
∠e = 108⁰, 
∠f =  72⁰, 
∠g = 108⁰,
∠h = 72⁰, 

Explanation:
Given ∠h = 72⁰, As ∠e = 180⁰ – 72⁰ = 108⁰, 
∠h = 72⁰ = ∠f = 72⁰, ∠g = 180⁰ – 72⁰ = 108⁰, ∠e = ∠a = 108⁰,
 ∠b = 180⁰ – 108⁰ = 72⁰,  ∠c = ∠g = 108⁰, ∠d = 180⁰ – 108⁰ = 72⁰.
Therefore ∠a = 108⁰,  ∠b = 72⁰, ∠c = 108⁰, ∠d = 72⁰,
∠e = 108⁰,  ∠f =  72⁰,  ∠g = 108⁰, ∠h = 72⁰..

Question 2:
Angle 3 is 48 degrees. List the measurements of the other seven angles.

∠1 = _________
∠2 = _________
∠3 = _________
∠4 = _________
∠5 = _________
∠6 = _________
∠7 = _________
Answer:
∠1 = 48⁰, 
∠2 = 132⁰,
∠3 = 48⁰,
∠4 = 132⁰,
∠5 = 48⁰, 
∠6 =  132⁰, 
∠7 = 48⁰,
∠8 = 132⁰, 

Explanation:
Given ∠3 = 48⁰, As ∠4 = 180⁰ – 48⁰ = 132⁰, 
∠1 = ∠3 = 48⁰, ∠2 = 180⁰ – 48⁰ = 132⁰,
∠5 = ∠1 = 48⁰,  ∠6 = 180⁰ – 48⁰ = 132⁰,
 ∠7 = ∠3 = 48⁰, ∠8 = 180⁰ – 108⁰ = 132⁰.
Therefore ∠1 = 48⁰,  ∠2 = 132⁰, ∠3 = 48⁰, ∠4 = 132⁰,
∠5 = 48⁰,  ∠6 =  132⁰,  ∠7 = 48⁰, ∠8 = 132⁰, 

Question 3.

Fill in the angle measurements for the other seven angles.
∠a = _________
∠b = _________
∠c = _________
∠d = _________
∠e = _________
∠g = _________
∠h = _________
Answer:
∠a = 125⁰, 
∠b = 55⁰,
∠c = 125⁰,
∠d = 55⁰,
∠e = 125⁰, 
∠g = 125⁰,
∠h = 55⁰, 

Explanation:
Given ∠f = 55⁰, So ∠g = 180⁰ – 55⁰ = 125⁰, 
∠g = ∠e = 125⁰, ∠h = 180⁰ – 125⁰ = 55⁰,
∠e = ∠a = 125⁰,  ∠b = 180⁰ – 125⁰ = 55⁰,  ∠c = ∠g = 125⁰,
∠d = 180⁰ – 125⁰ = 55⁰.
Therefore ∠a = 125⁰,  ∠b = 55⁰, ∠c = 125⁰, ∠d = 55⁰,
∠e = 125⁰,  ∠g = 125⁰, ∠h = 55⁰,

Question 4.

What is the measurement of ∠FOE? ______________
What is the measurement of ∠EOC? ______________
What is the measurement of ∠BOC? ______________
Answer:
The measurement of ∠FOE is 46⁰,
The measurement of ∠EOC is 90⁰,
The measurement of ∠BOC is 45⁰,

Explanation:
Given figure the measurement of ∠FOE is 46⁰ as
∠EOG = 90⁰ and given ∠FOG = 44⁰ , so therefore
∠FOE = ∠EOG – ∠FOG = 90⁰ – 44⁰ = 46⁰.
The measurement of ∠EOC is 90⁰ as ∠EOC = ∠EOG = 90⁰.
Now the measurement of ∠BOC is 45⁰ as ∠COA = 90⁰ = ∠AOB  + ∠BOC,
So ∠BOC = 90⁰ – ∠AOB  = 90⁰ – 45⁰ = 45⁰.